You may think that the appropriate estimate $\widehat{\sigma}$ of $\sigma$ is the RMSE. Very close! However, nottttt quite. We'll see when we cover the *bias-variance tradeoff* that the following holds

$$

\mbox{MSE} = \left(\mbox{Bias}\left[\widehat{f}(x)\right]\right)^2

+\mbox{Var}\left[\widehat{f}(x)\right] + \sigma^2

$$

where $\sigma^2$ is the variance of the error term $\epsilon$. Stay tuned!

##How to pick optimal degrees of freedom $df^*$

The optimal degrees of freedom $df^*$ here is 19. For a semi-arbitrarily chosen

"tolerance" of 0.05 RMSE units, the simplest model that yields similar

performance is $df=11$, since in the case of splines, "simpler" means fewer